Multifractal formalism for expanding rational semigroups and random complex dynamical systems
Dynamical Systems
2015-07-14 v4 Complex Variables
Abstract
We consider the multifractal formalism for the dynamics of semigroups of rational maps on the Riemann sphere and random complex dynamical systems. We elaborate a multifractal analysis of level sets given by quotients of Birkhoff sums with respect to the skew product associated with a semigroup of rational maps. Applying these results, we perform a multifractal analysis of the H\"older regularity of limit state functions of random complex dynamical systems.
Cite
@article{arxiv.1311.6241,
title = {Multifractal formalism for expanding rational semigroups and random complex dynamical systems},
author = {Johannes Jaerisch and Hiroki Sumi},
journal= {arXiv preprint arXiv:1311.6241},
year = {2015}
}